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Application of Portfolio Performance Measures 1129

portfolio (fund) should receive for its systematic risk using the following expected return equation for this period (22.96 percent is the return on the S&P 500 during this period, as shown in Exhibit 26.6):

The required return for risk simply is the latter term in this expression: p,(17.68). The required return for risk for Gabelli Asset Fund was 0.815(17.68) = 14.41 percent (its total required return is (5.28 + 14.41 = 19.69). The return for selectivity is the difference between overall performance (19.67 - 5.28 = 14.39) and the required return for risk (14.41). If the overall performance exceeds the required return for risk, the portfolio has experienced a positive return for selectivity. The results indicate that Gabelli Asset actually had an average annual return of -0.02 percent for selectivity (14.39 - 14.41). Seven funds had positive returns for selectivity (e.g., Kemper Technology Fund). In contrast, several funds had positive overall performance, but their required return for risk exceeded this figure, giving them negative returns for selectivity.

The next two columns in Exhibit 26.10 indicate the effect of diversification on performance. The diversification term indicates the required return for not being completely diversified (i.e., having total risk above systematic risk). If a fund's total risk is equal to its systematic risk, then the ratio of its total risk to the market's total risk will equal its beta. If this is not the case, then the ratio of the fund's total risk for the fund relative to the market will be greater than its beta, which implies an added return required because of incomplete diversification. For Gabelli Asset, the ratio of total risk was

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